A new television ad from Mitt Romney’s campaign shows how much the presidential election in Ohio is still turning on the battle to shape voter opinion of the Obama administration’s auto bailout. It has also revived a campaign debate over plans by Chrysler Corp.’s Jeep unit to build cars in China.

The new ad, which aired over the weekend in Ohio, challenges President Barack Obama’s effort to take credit for saving U.S. auto jobs with his government-backed rescues of General Motors Co. and Chrysler. The ad aired as a new poll for Ohio newspapers suggested that the race for Ohio’s 18 electoral votes is a dead heat.

The new Romney ad, which features nostalgic images of people enjoying rides in their cars, and then autos getting crushed at a junkyard, states that Mr. Obama “took GM and Chrysler into bankruptcy, and sold Chrysler to Italians who are going to build Jeeps in China.” (You can see it here.)

The ad draws on the fact that Chrysler and its Italian parent Fiat S.p.A, are in talks to build a Jeep assembly plant in China to serve growing demand for Jeep models there.

The Obama campaign cried foul. In responding to the ad, it noted that last week Mr. Romney had made the more aggressive statement that Jeep was planning to move all production to China, which Chrysler says is not the case. The Obama campaign accused Mr. Romney of “trying to scare Ohioans.”

Mr. Romney, in Defiance, Ohio, last week, told supporters: “One of the great manufacturers in this state, Jeep, now owned by the Italians, is thinking of moving all production to China. I will fight for every good job in America.”

Defiance is a manufacturing town in northwest Ohio not far from Toledo, which is home to a large Jeep assembly plant that Chrysler is spending $500 million to retool for a new Jeep Liberty model.

Shortly before Mr. Romney spoke, Chrysler’s chief spokesman, Gualberto Ranieri, had written on the company’s blog that Chrysler had no intention of shifting U.S. Jeep production to China.

China is the world’s largest auto market and and the second-largest for the Jeep brand, behind North America. Fiat and Chrysler executives have been signaling their desire to revive Jeep production in China for months—while at the same time hiring more workers at Jeep factories in Detroit and Toledo to meet robust demand for the Wrangler and Grand Cherokee sport utility vehicles.

Chrysler employs about 1,929 workers at the Toledo plant and 3,075 at the Jefferson North Jeep assembly plant in Detroit. The company has announced plans to hire an additional 1,100 workers in Detroit.

In his online statement, Mr. Ranieri was responding not to the Romney campaign ads or Mr. Romney’s comments, but to blogs that had misinterpreted a Bloomberg News story about the company’s plans to build Jeeps in China.

“Despite clear and accurate reporting,” Mr. Ranieri wrote, “the take has given birth to a number of stories making readers believe that Chrysler plans to shift all Jeep production to China from North America, and therefore idle assembly lines and U.S. workforce. It is a leap that would be difficult even for professional circus acrobats.

United Auto Workers union President Bob King, whose union represents workers at Chrysler’s Ohio factories, said Mr. Romney should “take personal responsibility for perpetuating a deplorable and false statement about Chrysler, a U.S. automaker that has bounced back in a big way after bankruptcy.”

So far, the Romney campaign hasn’t issued a public statement on the flap.

“To be truly successful in China and to truly grow your volume business, which we are, you have to be localized, you have to be able to produce models locally,” Mike Manley, head of the Jeep brand, said in a recent interview with The Wall Street Journal. “The future for Jeep has to be on a local basis.”

Most global auto makers – including Chrysler’s U.S. rivals GM and Ford Motor Co. – have extensive manufacturing operations in China, almost entirely focused on serving demand in China. Jeeps sent to China from the U.S. are subject to tariffs.

This wouldn’t be the first time Jeeps were built in China. Starting in the late 1980s, Jeeps were produced in Beijing under a joint venture deal Chrysler inherited from American Motors Corp. After Germany’s Daimler AG acquired Chrysler, that plant was switched to producing Mercedes vehicles.

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